Question

1. a sphere has a volume of ( 904.32 mathrm{~cm}^{3} ). what is its radius? use ( pi approx 3.14 ).

a. ( 7 mathrm{~cm} )
b. ( 5 mathrm{~cm} )
c. ( 4 mathrm{~cm} )
d. ( 6 mathrm{~cm} )

Explanation:

Step1: Recall the volume formula for a sphere

The volume formula for a sphere is \(V=\frac{4}{3}\pi r^{3}\).

Step2: Substitute the given values into the formula

We know \(V = 904.32\space cm^{3}\) and \(\pi\approx3.14\). So, \(904.32=\frac{4}{3}\times3.14\times r^{3}\).
First, simplify \(\frac{4}{3}\times3.14=\frac{12.56}{3}\). Then the equation becomes \(904.32=\frac{12.56}{3}r^{3}\).
Multiply both sides by \(3\) to get \(904.32\times3 = 12.56r^{3}\). So, \(2712.96=12.56r^{3}\).
Divide both sides by \(12.56\): \(r^{3}=\frac{2712.96}{12.56}=216\).

Step3: Solve for \(r\)

Take the cube - root of both sides. Since \(r^{3}=216\), then \(r = \sqrt[3]{216}\). And \(\sqrt[3]{216}=6\).

Answer:

d. \(6\space cm\)